Problem: Which of the following numbers is a multiple of 9? ${44,54,75,88,97}$
The multiples of $9$ are $9$ $18$ $27$ $36$ ..... In general, any number that leaves no remainder when divided by $9$ is considered a multiple of $9$ We can start by dividing each of our answer choices by $9$ $44 \div 9 = 4\text{ R }8$ $54 \div 9 = 6$ $75 \div 9 = 8\text{ R }3$ $88 \div 9 = 9\text{ R }7$ $97 \div 9 = 10\text{ R }7$ The only answer choice that leaves no remainder after the division is $54$ $ 6$ $9$ $54$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $54$ $54 = 2\times3\times3\times3 9 = 3\times3$ Therefore the only multiple of $9$ out of our choices is $54$. We can say that $54$ is divisible by $9$.